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arXiv · 2306.15565

A proof of Guo-Wang's conjecture on the uniqueness of positive harmonic functions in the unit ball

Pingxin Gu·Haizhong Li
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Abstract

Guo-Wang [Calc.Var.Partial Differential Equations,59(2020)] conjectured that for $1<q<\frac{n}{n-2}$ and $0<\lambda\leq \frac{1}{q-1}$, the positive solution $u\in C^{\infty}(\bar B)$ to the equation \[ \left\{ \begin{array}{ll} \Delta u=0 &in\ B^n,\\ u_{\nu}+\lambda u=u^q&on\ S^{n-1}, \end{array} \right. \] must be constant. In this paper, we give a proof of this conjecture.

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Pingxin Gu, Haizhong Li. 2023-06-27. A proof of Guo-Wang's conjecture on the uniqueness of positive harmonic functions in the unit ball. https://arxiv.org/abs/2306.15565

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